3. A finite region is bounded by the curve with equation \(y = x + x ^ { - \frac { 3 } { 2 } }\), the \(x\)-axis and the lines \(x = 1\) and \(x = 2\) This region is rotated through \(2 \pi\) radians about the \(x\)-axis. Show that the volume generated is \(\pi ( a \sqrt { 2 } + b )\), where \(a\) and \(b\) are rational numbers to be determined.
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